prompts in python are not saved it the database

Hello!

So I was using llm to make requests using the python api, and it seems that the prompts used in the python api are not saved into the database.
For me it was the expected behavior, because the docs says "llm defaults to logging all prompts and responses to a SQLite database.", and nothing on the python API page nor the Logging to SQLite.
Is this intended and not documented, a bug, or am I missing something?

small reproducible test:
test.py:

import llm

model = llm.get_model("gpt-4o-mini")
response = model.prompt("Five surprising names for a pet pelican")
print(response.text())

1. uv init && uv add llm
2. uv run llm logs -n 1 -> output your last message
3. uv run test.py -> print 5 names
4. uv run llm logs -n 1 -> should print "Five surprising names for a pet pelican" and the answer, print the same as 2.

Otherwise, thank you very much for your amazing work, it really helps me a lot!

Start with the reproducible test.py example and run the two uv run llm logs -n 1 commands around model.prompt(...) to confirm the difference between CLI and Python API logging. Trace the Python API logging path and SQLite persistence behavior. Done means the prompt and response from the Python API appear in llm logs, or the documentation clearly explains that they are intentionally excluded.